Financial Risk Modelling and Portfolio Optimization with R

Preface xi

List of abbreviations xiii

Part I MOTIVATION 1

1 Introduction 3

2 A brief course in R 6

2.1 Origin and development 6

2.2 Getting help 7

2.3 Working with R 10

2.4 Classes, methods and functions 12

2.5 The accompanying package FRAPO 20

3 Financial market data 26

3.1 Stylized facts on financial market returns 26

3.2 Implications for risk models 32

4 Measuring risks 34

4.1 Introduction 34

4.2 Synopsis of risk measures 34

4.3 Portfolio risk concepts 39

5 Modern portfolio theory 43

5.1 Introduction 43

5.2 Markowitz portfolios 43

5.3 Empirical mean-variance portfolios 47

Part II RISK MODELLING 51

6 Suitable distributions for returns 53

6.1 Preliminaries 53

6.2 The generalized hyperbolic distribution 53

6.3 The generalized lambda distribution 56

6.4 Synopsis of R packages for the GHD 62

6.5 Synopsis of R packages for GLD 67

6.6 Applications of the GHD to risk modelling 69

6.7 Applications of the GLD to risk modelling and data analysis 78

7 Extreme value theory 84

7.1 Preliminaries 84

7.2 Extreme value methods and models 85

7.3 Synopsis of R packages 89

7.4 Empirical applications of EVT 98

8 Modelling volatility 112

8.1 Preliminaries 112

8.2 The class of ARCH models 112

8.3 Synopsis of R packages 116

8.4 Empirical application of volatility models 123

9 Modelling dependence 127

9.1 Overview 127

9.2 Correlation, dependence and distributions 127

9.3 Copulae 130

9.4 Synopsis of R packages 136

9.5 Empirical applications of copulae 142

Part III PORTFOLIO OPTIMIZATION APPROACHES 153

10 Robust portfolio optimization 155

10.1 Overview 155

10.2 Robust statistics 156

10.3 Robust optimization 160

10.4 Synopsis of R packages 166

10.5 Empirical applications 171

11 Diversification reconsidered 189

11.1 Introduction 189

11.2 Most diversified portfolio 190

11.3 Risk contribution constrained portfolios 192

11.4

Bernhard Pfaff studied economics at the universities of Göttingen, Germany; Davis, California; and Freiburg im Breisgau, Germany. He obtained a diploma and a doctorate degree at the economics department of the last one where he was employed as a research and teaching assistant. He has worked for many years as economist and quantitative analyst in research departments of financial institutions. Bernhard Pfaff is the author and maintainer of the contributed R package "urca".